Abstract

In this article, particle kinetic equations which incorporate the nonlinear wave–particle interaction, as derived in P. H. Yoon [Phys. Plasmas 7, 4858 (2000)] and V. N. Tsytovich [Theory of Turbulent Plasma (Consultants Bureau, New York, 1977), pp. 103–110] are re-examined. A unified formalism is obtained after discrepancies in both references are resolved. The present particle kinetic equation is valid for the velocity space which does not satisfy the linear wave–particle resonance condition, ω−k⋅v≠0, but when the particle velocity of interest primarily satisfies the nonlinear wave–particle resonance, ω−ω′−(k−k′)⋅v=0.